Most fathers would probably cite the same qualities — and employ much the same language — if asked that very question. A dad provides, most would say. A dad protects. He tries to teach — often by example, if only because so many fathers still embrace that hoary old “strong, silent” stereotype, and so many dads find that showing rather than telling can frequently be a more eloquent method for imparting a lesson. (Or, at least, that’s what we like to tell ourselves when our kids just won’t freaking listen.)

In fact, of all the familial “hoods” — motherhood, childhood, fatherhood — the latter has probably changed less, in fundamental ways, than the others over the last several generations. Motherhood is largely unrecognizable (in so many positive ways) from the institution of, say, the 1950s, while childhood sometimes seems to be redefined with each new alarmist magazine cover: Our kids are too lazy! Our kids are too busy! Our kids are too coddled! Our kids are too stressed!

But fatherhood? For the most part, today’s dads are still bumbling good-naturedly along, much as their fathers and their fathers’ fathers did — maybe a little more “enlightened,” more “sensitive,” more “attuned” than their old men, but generally working on the same basic principles: Raise good kids. Don’t spoil them. Help them stand up and, every once in a while, let them fall down. Love them, guide them — and then, as painful as it’s going to be, let them go.

Here, on Father’s Day — just as we did on Mother’s Day — LIFE.com celebrates the holiday by taking a look at the rich and the famous. And, as we did on Mother’s Day, we’ll unabashedly offer up this disclaimer: the focus of the gallery is absolutely not meant to suggest that famous dads are more worthy of esteem than other dads. Instead, we’re publishing these portraits of famous dads with their kids, quite frankly, as a simple acknowledgement that, like most everybody else in the world, we’re fans. We’re fascinated by fame. And if a gallery featuring the likes of Steve McQueen, Humphrey Bogart, Robert Redford and other famous dads and their children isn’t quite the sober, reverential paean to fatherhood that people expect or want to see on the third Sunday in June … what can we say? Maybe next year we’ll do it differently. (But probably not.)